Applications of fractional calculus in solving Abel-type integral equations: Surface-volume reaction problem

TL;DR

This paper explores the application of fractional calculus to solve Abel-type integral equations arising from surface-volume reactions in optical biosensors, demonstrating the method's effectiveness in real-world modeling.

Contribution

It introduces a novel application of fractional calculus to a class of integro-differential equations, including the first instance of an unconventional fractional derivative order in an applied context.

Findings

Successful solution of fractional integro-differential equations

Identification of a new fractional derivative order in applications

Enhanced understanding of fractional calculus in biosensor modeling

Abstract

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed. Furthermore, for the first time, we encounter an order of the fractional derivative other than $\frac{1}{2}$ in an applied problem. Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional calculus.